This paper studies optimal household behaviour in a model of creative destr
uction. The saving technology is characterised by stochastic returns that f
ollow a Poisson process. It is shown that equilibrium conditions with optim
ising households differ substantially from equilibrium conditions where inv
estment in R&D is determined bl;firms. Three out of four market failures di
sappear and a new market failure resulting from a complementarity in financ
ing R&D is identified. Studying the social optimum shows that it contains a
s the special case of risk neutrality the social optimum derived in the lit
erature.